Free In-Plane Vibration of Circular Arches

by Anestis S. Veletsos, Brown and Root Prof. of Engrg. and Chmn.; Dept. of Civ. Engrg., Rice Univ., Houston, TX,
Walter J. Austin, Prof. of Civ. Engrg.; Rice Univ., Houston, TX,
Carlos A. Lopes Pereia, Prof. and Coordinator of Grad. Studies; Dept. of Civ. Engrg., Catholic Univ. of Rio de Janeiro, Brazil,
Shyr-Jen Wung, Formerly, Graduate Student; Dept. of Civ. Engrg., Rice Univ., Houston, TX,

Serial Information: Journal of the Engineering Mechanics Division, 1972, Vol. 98, Issue 2, Pg. 311-329

Document Type: Journal Paper


A comprehensive numerical study is made of the natural frequencies and modes of vibration of hinged and fixed, uniform, circular arches vibrating in their own plane. Based on a study of modal patterns and the distribution of the associated strain energies, it is shown that the vibrational modes may be almost purely flexural as in a beam, or almost purely extensional either as in a ring executing a uniform in-and-out motion or as in a bar in axial vibration, or the extensional and flexural actions may be strongly coupled. The conditions of occurrence of each type of behavior are defined, and simple approximate formulas are presented with the aid of which the free vibrational characteristics of such systems may be estimated readily. The approach used to derive the approximate formulas may also be applied to arches with other profiles, boundaries, and properties. The study is based on a theory which accurately considers all effects except rotatory inertia and shearing deformation.

Subject Headings: Numerical analysis | Vibration | Arches | Flexural strength | Numerical methods | Natural frequency | Hinges | Axial forces

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